Problem: Express your answer as a mixed number simplified to lowest terms. $14\dfrac{1}{3}-7\dfrac{16}{17} = {?}$
Find a common denominator for the fractions: $= {14\dfrac{17}{51}}-{7\dfrac{48}{51}}$ Convert ${14\dfrac{17}{51}}$ to ${13 + \dfrac{51}{51} + \dfrac{17}{51}}$ So the problem becomes: ${13\dfrac{68}{51}}-{7\dfrac{48}{51}}$ Separate the whole numbers from the fractional parts: $= {13} + {\dfrac{68}{51}} - {7} - {\dfrac{48}{51}}$ Bring the whole numbers together and the fractions together: $= {13} - {7} + {\dfrac{68}{51}} - {\dfrac{48}{51}}$ Subtract the whole numbers: $=6 + {\dfrac{68}{51}} - {\dfrac{48}{51}}$ Subtract the fractions: $= 6+\dfrac{20}{51}$ Combine the whole and fractional parts into a mixed number: $= 6\dfrac{20}{51}$